Bellazzini, Jacopo and Bonanno, Claudio (2010) Nonlinear Schrödinger equations with strongly singular potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 140 (4), p. 707-721. eISSN 1473-7124. Article.
Full text not available from this repository.
We look for standing waves for nonlinear Schrödinger equations
i ∂ψ/∂t +Δψ − g(|y|)ψ −W' (|ψ|) ψ /|ψ| = 0
with cylindrically symmetric potentials g vanishing at infinity and non-increasing, and a C1 nonlinear term satisfying weak assumptions. In particular, we show the existence of standing waves with non-vanishing angular momentum with prescribed L2 norm. The solutions are obtained via a minimization argument, and the proof is given for an abstract functional which presents a lack of compactness. As a specific case, we prove the existence of standing waves with non-vanishing angular momentum for the nonlinear hydrogen atom equation.
I documenti depositati in UnissResearch sono protetti dalle leggi che regolano il diritto d'autore
Repository Staff Only: item control page